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Proceedings of the American Mathematical Society

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Representing a differentiable function as a Cartesian product


Author: Michael R. Colvin
Journal: Proc. Amer. Math. Soc. 89 (1983), 523-526
MSC: Primary 55M20
DOI: https://doi.org/10.1090/S0002-9939-1983-0715879-3
MathSciNet review: 715879
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Abstract: This article produces an elementary proof of a result originally stated without proof by J. Leray. The main result gives conditions so that a continuously differentiable map from a product neighborhood of the origin in $ {{\mathbf{R}}^n}$ into $ {{\mathbf{R}}^n}$ can be homotoped to a cartesian product of maps on intervals. The resulting product function preserves properties of the original map near the origin.


References [Enhancements On Off] (What's this?)

  • [AR] R. Abraham and J. Robbin, Transversal mappings and flows, Benjamin, New York, 1967. MR 0240836 (39:2181)
  • [B$ _{1}$] R. F. Brown, An elementary proof of the uniqueness of the fixed point index, Pacific J. Math. 35 (1970), 549-558. MR 0281197 (43:6916)
  • [B$ _{2}$] -, The Lefschetz fixed point theorem, Scott, Foresman, Chicago, Ill., 1971. MR 0283793 (44:1023)
  • [B$ _{3}$] -, Notes on Leray's index theory, Adv. in Math. 7 (1971), 1-28. MR 0296933 (45:5992)
  • [Le] S. Leray, Sur les équations et les transformations, J. Math. Pures Appl. 24 (1945), 201-248.
  • [W] H. Whitney, Analytic extensions of differentiable functions defined on closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89. MR 1501735

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0715879-3
Keywords: Fixed point theory, index, jacobian, Whitney extension theorems, inverse function theorem
Article copyright: © Copyright 1983 American Mathematical Society

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